Correctness and Relative Correctness

In the process of trying to define what is a software fault, we have found that to formally define software faults we need to introduce the concept of relative correctness, i.e. the property of a program to be more-correct than another with respect to a given specification. A feature of a program is a fault (for a given specification)only because there exists an alternative to it that would make the program more-correct with respect to the specification.In this paper, we explore applications of the concept of relative correctness in program testing, program repair, and program design.Specifically, we argue that in many situations of software testing, fault removal and program repair, testing for relative correctness rather than absolute correctness leads to clearer conclusions and better outcomes. Also, we find that designing programs by stepwise correctness-enhancing transformations rather than by stepwise correctness-preserving refinements leads to simpler programs and is more tolerant of designer mistakes.